Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 7 - Analytic Trigonometry - 7.4 Trigonometric Identities - 7.4 Assess Your Understanding: 11

Answer

$\frac{1}{cos\theta}$

Work Step by Step

The identity says: $tan(\theta)=\frac{sin\theta}{cos\theta}$ and $csc(\theta)=\frac{1}{sin(\theta)}$. Hence $tan(\theta)\cdot csc(\theta)=\frac{sin\theta}{cos\theta}\cdot \frac{1}{sin(\theta)}=\frac{1}{cos\theta}$
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